symbolic.limit wrongly gives ZeroDivisionError

[dkrenn]

We have

sage: (4-x^2)/(3-sqrt(x^2+5)).limit(x=2)
Traceback (most recent call last):
...
ZeroDivisionError: Symbolic division by zero

but

sage: limit((4-x^2)/(3-sqrt(x^2+5)), x=2)
6

Those two should give the same result (at least the docstring of x.limit says See "sage.calculus.calculus.limit", so it has the appearence that the same functions are called).

CC: @kcrisman

Component: symbolics

Keywords: symbolic, limit, wrong, zero division

Reviewer: Daniel Krenn, Akshay Ajagekar

Issue created by migration from https://trac.sagemath.org/ticket/15451

[dkrenn]

comment:5

Still there in 6.6.

[sagetrac-ajagekar-akshay]

comment:6

I don't understand the issue. In case of

sage: (4-x^2)/(3-sqrt(x^2+5)).limit(x=2)

4-x^2 gets divided by (3-sqrt(x^2+5)).limit(x=2) which is 0, so the ZeroDivisionError. But this works

sage: ((4-x^2)/(3-sqrt(x^2+5))).limit(x=2)
6

[rwst]

comment:7

Well, it's similar to (sin(x)/x).limit(x=0), isn't it?

https://en.wikipedia.org/wiki/Indeterminate_form

[sagetrac-ajagekar-akshay]

comment:8

The expression of which limit is evaluated in this case is (3-sqrt(x^2+5)) at x=2 and not the whole expression (4-x<sup>2)/(3-sqrt(x</sup>2+5)) as for the second case limit((4-x<sup>2)/(3-sqrt(x</sup>2+5)), x=2) limit is evaluated for whole expression. proper parenthesis would give correct answer.

[rwst]

comment:9

So you agree it's user error?